Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Evie's flashcards > Trigonometry > Flashcards

Trigonometry Flashcards

1
Q

What is the Pythagorean theorem?

A

In a right triangle, a² + b² = c², where c is the hypotenuse.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What are the primary trigonometric ratios?

A

Sine, Cosine, and Tangent.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is the sine of an angle in a right triangle?

A

The ratio of the length of the opposite side to the hypotenuse.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the cosine of an angle in a right triangle?

A

The ratio of the length of the adjacent side to the hypotenuse.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the tangent of an angle in a right triangle?

A

The ratio of the length of the opposite side to the adjacent side.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

True or False: The sine function is defined for all angles.

A

True.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Fill in the blank: In a right triangle, tan(θ) = _____.

A

opposite/adjacent.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is the range of the sine function?

A

[-1, 1].

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the range of the cosine function?

A

[-1, 1].

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is the range of the tangent function?

A

All real numbers.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the formula for finding the hypotenuse using sine?

A

hypotenuse = opposite/sine(θ).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is the formula for finding the opposite side using cosine?

A

opposite = hypotenuse * sine(θ).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is the cosine of 0 degrees?

A

1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the sine of 90 degrees?

A

1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the value of tan(45 degrees)?

A

1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What does SOHCAHTOA stand for?

A

Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

If sin(θ) = 1/2, what is θ in degrees?

A

30 degrees or 150 degrees.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

If cos(θ) = 0, what are the possible angles for θ?

A

90 degrees or 270 degrees.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

How do you convert radians to degrees?

A

Multiply by 180/π.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is the value of sin(180 degrees)?

A

0.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is the value of cos(180 degrees)?

A

-1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is the sine rule?

A

a/sin(A) = b/sin(B) = c/sin(C), where a, b, c are sides and A, B, C are opposite angles.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is the cosine rule?

A

c² = a² + b² - 2ab*cos(C).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

True or False: The sine function is periodic.

A

True.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

What is the period of the sine function?

A

360 degrees or 2π radians.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

What is the period of the cosine function?

A

360 degrees or 2π radians.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

What is the period of the tangent function?

A

180 degrees or π radians.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

What is the reference angle for 210 degrees?

A

30 degrees.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

What is the reference angle for 330 degrees?

A

30 degrees.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

True or False: The tangent function is undefined at 90 degrees.

A

True.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

What is the value of sin(270 degrees)?

A

-1.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

If tan(θ) = 0, what is θ?

A

0 degrees, 180 degrees, or any multiple of 180 degrees.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

What is the value of cos(90 degrees)?

A

0.

34
Q

What is the value of sin(360 degrees)?

A

0.

35
Q

Fill in the blank: The opposite side is opposite to the _____.

A

angle.

36
Q

What is the hypotenuse in a 3-4-5 triangle?

A

5.

37
Q

What is the length of the adjacent side in a triangle with an angle of 30 degrees and hypotenuse of 10?

A

√3 * 5 (approximately 8.66).

38
Q

If sin(θ) = 0.5, what is the value of θ in radians?

A

π/6 or 5π/6.

39
Q

What is the tangent of 30 degrees?

A

1/√3 or √3/3.

40
Q

What is the cosine of 45 degrees?

A

√2/2.

41
Q

What quadrant is sin positive and cos negative?

A

Quadrant II.

42
Q

What quadrant is tan positive?

A

Quadrant I and III.

43
Q

What is the sine of 60 degrees?

A

√3/2.

44
Q

What is the cosine of 30 degrees?

A

√3/2.

45
Q

What is the tangent of 60 degrees?

A

√3.

46
Q

Fill in the blank: The law of sines can be used in non-right triangles using the formula _____.

A

a/sin(A) = b/sin(B) = c/sin(C).

47
Q

Fill in the blank: The law of cosines is used to find a side when you know _____.

A

two sides and the included angle.

48
Q

True or False: The sum of angles in a triangle is always 180 degrees.

A

True.

49
Q

What is the formula for finding the area of a triangle using sine?

A

Area = 1/2 * a * b * sin(C).

50
Q

What is the value of sin(45 degrees)?

A

√2/2.

51
Q

What is the length of the opposite side in a triangle with an angle of 60 degrees and hypotenuse of 8?

A

4√3 (approximately 6.93).

52
Q

What is the value of cos(0 degrees)?

A

1.

53
Q

What is the value of tan(0 degrees)?

A

0.

54
Q

What is the complementary angle of 30 degrees?

A

60 degrees.

55
Q

What is the complementary angle of 45 degrees?

A

45 degrees.

56
Q

What is the complementary angle of 60 degrees?

A

30 degrees.

57
Q

What is the exact value of sin(30 degrees)?

A

1/2.

58
Q

What is the exact value of cos(60 degrees)?

A

1/2.

59
Q

What is the exact value of tan(30 degrees)?

A

1/√3.

60
Q

What does it mean for two angles to be co-terminal?

A

They differ by a multiple of 360 degrees or 2π radians.

61
Q

What is the sine of an angle in the fourth quadrant?

A

Negative.

62
Q

What is the cosine of an angle in the second quadrant?

A

Negative.

63
Q

Fill in the blank: The sine of an angle is the same as the cosine of its _____.

A

complement.

64
Q

What is the angle of elevation?

A

The angle formed by the line of sight above the horizontal.

65
Q

What is the angle of depression?

A

The angle formed by the line of sight below the horizontal.

66
Q

What is the relationship between the sides in a 45-45-90 triangle?

A

The legs are equal, and the hypotenuse is √2 times a leg.

67
Q

What is the relationship between the sides in a 30-60-90 triangle?

A

The lengths are in the ratio 1:√3:2.

68
Q

What is the sine of 120 degrees?

A

√3/2.

69
Q

What is the cosine of 120 degrees?

A

-1/2.

70
Q

What is the tangent of 120 degrees?

A

-√3.

71
Q

True or False: The unit circle is used to define trigonometric functions.

A

True.

72
Q

Fill in the blank: The coordinates of a point on the unit circle can be expressed as (_____, _____).

A

cos(θ), sin(θ).

73
Q

What is the value of sin(π)?

A

0.

74
Q

What is the value of cos(π)?

A

-1.

75
Q

What is the value of tan(π/4)?

A

1.

76
Q

What is the formula for converting degrees to radians?

A

Multiply by π/180.

77
Q

What is the value of sin(1 radian) approximately?

A

0.84.

78
Q

What is the value of cos(1 radian) approximately?

A

0.54.

79
Q

What is the value of tan(1 radian) approximately?

A

1.56.

80
Q

What is the relationship between degrees and radians?

A

180 degrees = π radians.

81
Q

What is the value of sin(2π)?

A

0.

82
Q

What is the value of cos(2π)?

A

1.

Evie's flashcards (6 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions